Sunday, November 30, 2014

A Case for the Lydian Chromatic Concept

The
Lydian Chromatic Concept of Tonal Organization is a theory of Western music
developed by composer George Russell during an unfortunate but highly
productive bout of tuberculosis in 1945. Initially searching for the sonic
origin of chords, Russell devised the Concept as a means of accounting for and
remedying what he felt were inconvenient anomalies in the way that traditional
Western theory explained the music he heard around him.[1]
In the 61 years since the Lydian Chromatic Concept was first published, there
has been a delightful amount of controversy surrounding, and relatively little
support for, Russell’s theoretical opus. It is my intent to shed some light on
what I have found to be the virtue and methodical beauty of Russell’s concept
within our contemporary musical environment. Bear with me; it’ll be a lot of
fun.

To
make a brief explanatory voyage into my own background, I first became
interested in the Lydian Chromatic Concept as a graduate student at the New
England Conservatory of Music in Boston. While I had heard occasional mention
of the Concept since high school (most notably by my jazz guru, David
Schumacher, and in Robert Palmer’s liner notes to Kind of Blue), I began taking a close look at the theory in the
class that Professor Ben Schwendener had inherited from Mr. Russell himself. My
formal education prior to my years as an improvising trumpeter at the
Conservatory was in philosophy, and I took a special interest in the works of
Karl Popper and Thomas Kuhn in the Philosophy of Science. I brought the
critical attitude I had exercised in philosophy school to Lydian Chromatic
class, and I strove to find weaknesses in Russell’s concept while also
examining the shortcomings of conventional theory. As I continued to question
the Concept, I began to see the benefits to Russell’s approach in my thinking
as an improviser and composer, and I gained an appreciation for the freedom,
order, and power of explanation that I felt I was allowed. I have since studied
the Concept privately with the benevolent Professor Schwendener in an attempt
to gain a comprehensive grasp of Russell’s theory.

The reason I find myself writing this story now is
that I feel as though there is a value to the Lydian Chromatic Concept that
remains largely misunderstood and underappreciated by musicians and theorists.
Furthermore, I believe that George Russell only scratched the surface of the
possibilities of his approach, and the further development and fine-tuning of
the Concept will require the interest and scrutiny of my friends in the realm
of modern music (that’s where you come in). Lastly, I should add that if the
future explorations of my contemporaries should prove Russell’s Concept wholly
worthless, I say thank God; let’s try to waste as little time as possible on
any more convoluted nonsense.

Speaking of convolution, as we go forward I will
attempt to provide a summary of my thoughts with ample explanation of the
principles of the Concept as to be properly informative, but not so informative
as to turn this relatively innocuous article into a mind-numbingly elaborate
dissertation on what I know of Russell’s ideas. I would encourage everyone who
is theoretically inclined to, with an open mind and a critical attitude, read
through Russell’s Lydian Chromatic Concept of Tonal Organization in order to arrive at an independent conclusion on
the advantages and disadvantages to Russell’s approach.

Before beginning to wade into the Lydian Chromatic
Concept, let us first ask ourselves the fundamental question, “What the hell
are we doing studying music theory in the first place?” To properly explore
this inquiry, we might then ask, “What the hell are we doing studying theories
in general?” It occurs to me that one great advantage to the inquisitive nature
and analytical facility of our gigantic and enigmatic human brains is that if
we can figure out why things work the way they work, we can figure out ways to
manipulate those things to our advantage. The Germ Theory of Disease promoted
by Agostino Bassi, Louis Pasteur, et al. helped convince medical practitioners
that they could save lives by sterilizing their environments. The political
theory of John Locke helped pave the way for the practical rule of law provided
by the U.S. Constitution. Following this line of thought, we develop theories of music
to figure out why music sounds the way that it sounds as a means of finding
ways of writing good music.[2]

The beauty of the Lydian Chromatic Concept is that
its foundation lies in the objective physical properties of sound accounting
for twelve-tone equal temperament.[3]
Based on sonic principles, the Concept serves to allow us to explain why our music sounds the way that it sounds rather
than striving to codify musical convention. The foundation of the Concept is
the principle of tonal gravity, and the foundation of tonal gravity is the
overtone series.The idea is that
the interval of a perfect fifth, the “strongest” interval given its position as
the first interval after the octave in the overtone series, can be used to
produce a spectrum of tones with increasingly remote connections to an
established tonic pitch. Wow, I don’t know about you, but I’m excited already.
Check it out; based on an F as the tonic pitch, this spectrum of tones, the “Lydian
Chromatic Order of Tonal Gravity,” looks like this:

Let’s
start with F as the tonic. The first non-F in the overtones of an F is C. C has
a close relationship with F, and is highly consonant (hence, “perfect”). If we
start on this C, the first non-C overtone is a G, a perfect fifth above C. This
G is two degrees separated from the tonic F, but it still has a close
relationship with F and a consonant sound over the F and the C. If we start on
the G and find the first non-G overtone, we get D: three degrees from F, but
still relatively close and highly consonant.

Let’s
add the fifth tone in F’s order of tonal gravity. So far we have F, C, G, D,
and A. Rearranged, that gives us F, G, A, C, and D. These five tones make up
the F major pentatonic scale, a highly consonant scale used frequently in the
music of many cultures throughout the globe. Should we start this scale on the
D, we also get the very popular minor pentatonic scale. If we include the next
tone in F’s tonal gravity spectrum, E, we get a six-note scale resembling the
major scale, but without the fourth degree. We might find this scale used in
Western European folk music or by jazz students striving to avoid that
vexatious “avoid” note on a Maj7 chord. Note that these are also all of the
notes present in a fully voiced Maj13 chord.

All
right, here’s where people start losing their minds. If we ascend this order of
tonal gravity a perfect fifth from E, we get a B natural, six degrees from the
tonic F. Rearranged, these seven tones give us F, G, A, B, C, D, and E: the F
Lydian scale. Hence, the “Lydian” in “Lydian Chromatic” and the reason Russell
felt that Lydian, rather than Ionian, should be the mode at the root of his
theory of music. Due to the overtone-driven relationship between these seven tones
and the tonic, Russell described the Lydian scale as being in unity with its
tonic and felt as though it was the proper “parent scale” for what we know as
the seven modes of the major scale: Lydian, Mixolydian, Aeolian, Locrian,
Ionian, Dorian, and Phrygian. If you’re feeling like this whole#4 replacing the 4 situation is really rustling your jimmies, try
playing an FMaj7 chord on the piano and experiment with the different tones in
the order of tonal gravity as they become increasingly distant from the root. I
think you’ll find that the B natural sounds like it has a closer relationship
to the tonic than that feisty gremlin, the “avoid note.”[4]
All of this so far falls under the category of what Russell called “vertical
tonal gravity” because we are dealing with the relationships between tones and
a tonic pitch at one moment in time. Ok, that’s the majority of the technical
explanatory aspect of our adventure through Lydian Chromatic world and the
fundamental basis of the concept itself. I’ve got a little more to say on the
subject of tonal gravity before we move on. Thanks for your patience.

If
F natural were Kevin Bacon, the aforementioned sixth degree of separation would
be the end of the road for us.[5]
Alas, it is not, and we’ll carry on to the eighth tone in the order of tonal
gravity. If you take a glance at my diagram of the order of tonal gravity from
F outward, you’ll notice that after B, we skip a fifth and end up on C#, the #5, rather than F#. This hiccup in
the tonal spectrum would be impossible to explain within the reasonable
confines of this still fairly innocuous article, but I’ll summarize the oddity
by saying that it is a compromise that must be made for the twelve-tone equal
temperament that serves as the foundation of our Western harmonic language.To further clarify, Western music as we
know it depends on making adjustments to the natural overtone series and
dividing the octave into 12 equal parts so we can do fancy stuff like play in
tune over multiple octaves. This leap in the tonal order accounts for this, and
makes sense sonically in the long run. For now you’ll just have to trust me.

After
the #5, the rest of the order of tonal gravity continues
up in fifths until we reach the most distant tone from the F tonic, F#. This completes the pitch spectrum and gives us all of what George
Russell called the “Lydian Chromatic” scale. Following our example so far, the
F Lydian Chromatic scale contains all 12 notes in the F chromatic scale, each
of which has a distinct relationship, close to distant, from the tonic F to the
12th tone, F#. This concludes the wholly technical portion of
our program. For further reading on the technical specifics of the Concept,
read Russell’s book! I promise it’ll be a grand time.

“Ok
genius, so the Lydian scale should be regarded as the harmonic foundation of
Western music. What about Ionian? It clearly sounds a tonic, it seems to
produce the same chords as Lydian, it has had the major melodic role in music for centuries, and it
works great! Are you saying Bach was wrong?” Well, first of all, calm down, imaginary skeptic.
Second of all, conventional theory and the major scale occupy an important
place in the Lydian Chromatic Concept. Let’s keep in mind that we still use
Isaac Newton’s Classical Mechanics a hundred years after Einstein developed his
Theory of Relativity. The Concept doesn’t disprove anything or serve to show
conventional theory is useless or invalid; rather, it provides us with an
alternate paradigm from which to view conventional theory. As a brief overview
of this perspective, Russell considered the major scale to be a horizontal (goal-oriented) scale that consists of two vertical
(in unity with a tonic)
tetrachords. The first tetrachord resolves to the second tetrachord, giving us
a strong sense of resolution to the tonic in the same way that a IV chord
sounds a strong resolution to the I chord (amen, brother). See this example:

On
the one hand, this merged duality makes the major scale very functionally
useful, but this structure prevents Ionian from providing us with a unified
center of organization in the same way the Lydian parent scale does. The moral
of the story is that the Ionian mode occupies an important place in the Lydian
Chromatic Concept, albeit a more subsidiary place than it occupies in
conventional theory. Now we move on to the good stuff.

Why I like the Lydian Chromatic Concept

Explanation of Anomalies

The most initially apparent but relatively
superficial benefit to the Concept is that it accounts for sonic anomalies
inherent in the traditional method of theoretical analysis. There are two
problems especially evident in conventional jazz theory that are accounted for
by the Lydian Chromatic Concept. They are as follows:

Jazz educators the world over have been known to
suggest to young improvisers that the Ionian mode is the scale that most
closely corresponds to the ubiquitous Maj7 chord, but that the fourth degree
should be used in passing or avoided altogether. The same is said of the minor
sixth degree of the Aeolian mode over a minor chord. The explanation most often
given is simply that these notes sound bad, or more elaborately that the fourth
clashes with the third of the major chord, and the minor sixth clashes with the
fifth of the minor chord.

George
Russell postulated that the reason for the dissonance is that C Ionian, for
tonic example, is rooted in F Lydian, whereas a CMaj7 chord is rooted in C
Lydian, a perfect fifth away. Similarly, A Aeolian is rooted in F Lydian,
whereas an A minor or Amin7 chord is rooted in C Lydian, a perfect fifth away.
Russell elaborated on the power and popularity of the Ionian and Aeolian modes,
stating that by creating a melody using a mode whose parent scale is one fifth
below the chord to which the melody resolves, the improviser or composer is
implying a kind of plagal cadence that provides the music with a sense of
forward motion towards the tonic at the root of the chord at hand (again, F[IV] to C[I]). This idea has to do with “horizontal tonal
gravity” which deals with relationships between horizontal scales and an
underlying harmonic progression in time. By using the fourth degree of the
Ionian mode or the minor sixth degree of the Aeolian mode as a passing tone,
the musician is establishing a resolution to a tonic. However, by holding these
pitches over the major or minor chords with which they traditionally
correspond, the musician is accessing the rather dissonant 11th tone
of the tonal gravity spectrum of the chord at hand. In conclusion, provided
that we all agree with Russell’s assessment (and we don’t), we can finally
replace that sinister “avoid” note with the much friendlier “11tone
order/resolve to a tonic a fifth north of the parent scale” note. Well, I like
the sound of it, anyway.

By organizing modes by their parent scale
established in tonal gravity, it is easy to see the vertical and horizontal
relationships between various chords and scales. Let’s take the example of a
blues scale over a blues progression. The sound most closely associated with
the dominant 7th chords that make up your everyday major blues is
the Mixolydian mode. In Lydian Chromatic terms, C Mixolydian is the second mode
of its parent scale, Bb Lydian. The C blues scale so often tastefully
played over a C major blues is rooted in the sixth mode of its parent scale, EbLydian. EbLydian and BbLydian are a
perfect fifth apart in the same way that F Lydian and C Lydian are a fifth
apart. Just as C Ionian (F Lydian) resolves to CMaj7 (C Lydian) in the previous
anomaly, the C blues scale (Eb Lydian) provides a kind of
plagal cadence to C7 (Bb Lydian). As with the major scale, this idea deals
with horizontal tonal gravity, and the tonal relationship makes for a consonant
and tonic-seeking sound. Note that the same resolution could be found in an
example where the C blues scale is played over a CMaj7 chord, except that the
resolution would be three fifths from Eb Lydian to C
Lydian, rather than just one – a triple plagal cadence… or something like that.
There are many other practical examples that could be used to illustrate this
anomaly in conventional theory, but I think this common blues scale example
will be sufficient for now.[7]

Two
related notes on anomalies or limitations in conventional theory:

Throughout my discussion of sonic anomalies I have
referenced the idea that the sound of a resolving cadence is established when a
mode from one parent scale resolves to another parent scale x number of fifths
away, i.e. F Lydian to C Lydian, Eb Lydian to Bb Lydian, Eb Lydian to C Lydian. Coming from conventional jazz
theory, it seems intuitive to us that a standard ii-V-I progression would
contain three chords that all belong to the same key or parent scale. Using C
Major as an example, we have Dmin7 (ii of C) – G7 (V of C) – and C Major (I of
C). In Lydian Chromatic terms, a ii-V-I consists of one parent scale resolving
to another parent scale one fifth away: Dmin7 (vi of F Lydian) – G7 (II of F
Lydian) – C Major (I of C Lydian). In addition to the ever-important harmonic
rhythm and the motion of voices within the chords, Russell’s perspective gives
an explanation as to the forward-moving sound of such a cadential resolution.
The same could be said of another common example: Fmin7 (vi of Ab) – Bb7 (II of Ab) – C Major (I
of C), except that here, the resolution from parent scale (Ab) to parent scale (C) extends over not one but four fifths (Ab- Eb- Bb- F - C).
In retrospect it seems to me unusual that conventional theory wouldn’t account
for the sound of these cadential relationships, but I suspect many who read
this will think it crazy of me to treat a ii-V-I as consisting of two separate
parent scales. For this reason I’ve decided to include what I think to be an
oddity as an addendum rather than an anomaly in the system.

One
final note on conventional theory: Due to the fact that the Lydian Chromatic
Concept deals with sonic relationships rather than musical conventions, I have
found many unconventional or non-Western pieces of music relatively easy to
explain in Lydian Chromatic terms, but difficult to explain using traditional
Western theory. While many jazz standards and classical pieces can be as
effectively analyzed using conventional theory as the Lydian Chromatic Concept,
I have found it highly effective and enlightening to use the Concept when
dealing with the music of Charles Ives, Eric Dolphy, Arnold Schoenberg, Ornette
Coleman, Boban Markovic, Mulatu Astatke, Les Claypool, and others. In a post-20th
century world where accessible recording technology and advanced communication
systems are, to my great excitement, continually bringing music and musicians
together from so many cultures across the globe, I find it helpful to have
access to a theoretical approach that remains largely free from adherence to
particular stylistic conventions.

Creation and Liberation through Tonal Gravity

One great advantage to approaching composition
(spontaneous or premeditated) from a Lydian Chromatic perspective is that the
concept of tonal gravity allows for the calculated manipulation of parent
scales in order to arrive at particular modalities of varying degrees and
styles of dissonance.That is, by
replacing select pitches in lower tonal orders with pitches in higher tonal
orders, the musician has a great deal of control over a seemingly endless array
of modal colors. This allows for a great deal of sonic freedom and also
provides us with a practical and user-friendly system of modal organization.

Let’s return to our friend F Lydian, constructed of
the first seven pitches in the order of tonal gravity beginning on an F tonic.
If we take the eighth tone in the order, C#, and use it to
replace the C in F Lydian, we have the F Lydian Augmented scale:

With
F Lydian Augmented as our (eight tone order) parent scale, we have the
following seven modes:[8]

These
seven modes are traditionally referred to as the modes of the melodic minor
scale, and have been an important part of the jazz lexicon for at least 60
years. Now let’s take that ordinary F Lydian and replace the G with G#, the ninth tone in F’s tonal order. This gives us the following seven
modes based on the parent scale Lydian #2:

These
seven modes are traditionally referred to as the modes of the harmonic minor
scale, and have also been a fairly common sound in jazz since the ‘50’s and a
big part of Eastern European and Northern African music since time immemorial.

If
we take these three popular modes and organize them by their place in
conventional theory and their place in the Lydian Chromatic Concept, it is easy
to see the functional order in the Lydian Chromatic system:

I
use the aforementioned parent scales as examples because they illustrate the
way in which we can use the 7th, 8th, and 9th
tones in the order of tonal gravity to construct some common sounds. However,
be aware that this principle can also be used to come up with any number of
satisfyingly unusual parent scales and their modes. Anything goes, but two
other common examples include: whole tone (a hexatonic Lydian with a #5 and #6 [the 8th and 10th tones in
the order]) and diminished (an octatonic Lydian with a #5 [8th tone], b3 [9th
tone], and a n4 [11th tone]). One uncommon example
might be a heptatonic Lydian with a #2 [9th
tone] and a #6 [10th tone]. Russell referred to any
unconventional scale of any number of notes as an “official scale.” I like this
term because it’s as confusing as it is open-ended and accepting.

Creation

I
feel as though a foundation in Russell’s tonal organization has provided me
with a roadmap to the sonic wilderness. As a composer, I am able to use the
order of tonal gravity to explore new modal colors. If I discover a mode that I
like for the benefit of some conceptual or emotional end, the Concept will lead
me to the parent scale that serves as a foundation for the various other modal
colors available. As an example, let’s say I’m trying to compose a piece with a
sound similar to the following spooky, exotic mode:

Tonal
gravity will lead me to its Lydian #2 #6 parent scale:

From
here, if I were looking for an Ionianish version of this color to fit a major
or augmented chord, I might use the fifth mode of this Lydian parent scale:
Ionian #2 #5. If I were looking for a
spooky horizontal sound to accompany a minor chord, I could try the third mode:
Harmonic minor with a #4.

As
an improviser, I can choose to access the more distant tones in the parent
scale of any chord in order to explore some more unconventional sounds over
conventional chords. I may, as a common example, opt to use the eighth tone in
the order to play a Mixolydian #4 sound (second mode of
Lydian Augmented) instead of regular ol’ Mixolydian (second mode of Lydian)
over a standard dominant 7th chord. The sound is still related to
the chord at hand, but is a little farther out than what might in this context
be the more common choice. One could choose to alter any number of tones like
this until, to the Improv 101 professor’s great disdain, an inventive
improviser with a taste for the avant-garde is confidently justifying a
maniacal atonal tirade over “All of Me.”

Having
a perspective on the relationship between various parent scales also gives the
wily improviser options to superimpose certain modes over relatively unrelated
chords. In jazz pedagogy, one product of this idea is known as “side-stepping,”
and it most often involves playing a melody a half step above where it would
normally be played, and then resolving the melody back to the consonant chord
at hand. Looking at chords and melodies in terms of their respective parent
scales, the improviser can experiment with any combination of modal colors,
creating melodies that may seem to pull inward towards the tonic of a chord of
a different key, or float above the progression in a state of defiant
polytonality. Tonal gravity and the circle of fifths give us a handle on the
nature of the relationships between two or more modes, and why these
relationships have certain musical effects.

In
addition to providing us with a way of approaching the vertical relationships
between pitches, chords, and modes, another great advantage to the Lydian
Chromatic Concept is that it gives the composer a clear perspective of the
relationships between different chords in time. As was alluded to in previous
sections, the Concept looks at chords as being representations of modes, and
thus each chord can be found to belong to a Lydian parent scale. Looking at the
harmony of a piece of music in terms of the relationships between various
parent scales in time allows for an ease in analysis and exploration of
unconventional and pan-tonal chord progressions. This idea has compositional
and analytical implications that far outweigh the little space I’m able to
provide for it here, but an example of this kind of horizontal harmonic
analysis can be found back in my brief discussion of chord progressions in the
“Two related notes on anomalies…” section.

At the end of the day, our job as musical artists
is to use vibrations in the air to convey ideas and emotion, and our ears and imaginations are
our greatest tools. The Lydian Chromatic Concept simply provides a clear view
of the vast sea of sonic options at our disposal, which we may choose to use or
ignore.

Liberation

There are no wrong notes! Tonal gravity eliminates
the need for antiquated and oppressive dualistic distinctions like “right” or
“wrong” in music. Instead, we can look at tonal relationships on a spectrum
from consonant to dissonant. Perhaps one might find it useful to use “right”
and “wrong” to illustrate compositional concepts to young improvisers; however,
only the crankiest among us would still find it helpful to describe the music
of Sam Rivers or Woody Shaw as being peppered with “wrong notes.” I suppose we
could go by the old adage, “You have to learn the rules so you can break the
rules,” and argue that avant-minded composers and improvisers are expert rule
breakers. But who needs rules in the first place? I say rules be damned! Let the
impotent jazz police cry themselves to sleep as we venture headlong into the
sonic unknown, looking back at our forbears with a new sense of reverence and
admiration. Let us learn everything we can about how and why our music sounds
the way that it sounds so that we can be honest composers, building on the
tradition and inventing anew in order to reflect on our own place in time and
space. Let us take a new liberated dissonance and allow it freedom to stand
alongside consonance towards a common goal: the cultural and intellectual
evolution of mankind!

Ok, I may have gotten a little worked up there. In
summary, George Russell’s Lydian Chromatic Concept gives us a relatively
objective way to view the relationships between tonal colors in a 12 tone equal
tempered system without strict adherence to tradition or stylistic convention.
The Concept makes no comment on aesthetics or taste, so it is up to us, the
artists, to use what knowledge we can gain and, most importantly, our
intuition, to find ways of saying what we have to say. If we can learn anything
from the history of science and philosophical thought, we will someday find
more practical and accurate ways to approach music theory. However, in order to
reach new heights it is important to take the time to explore different
contemporary theoretical paradigms to glean from them what is helpful and what
is not. I have only scratched the surface of the explanatory scope, sonic
implications, and inherent philosophy of the Lydian Chromatic Concept, but I
hope to spur some small amount of interest in Russell’s ideas, or give an
answer to those who wonder why anybody has bothered to study this stuff in the
first place. At best, somebody out there will use a newfound interest or an
utter hatred for the Concept as fuel for some great new music. Regardless as to
the future of the theory itself, those familiar with the compositions and
improvisations of Miles Davis, Eric Dolphy, Art Farmer, David Baker, Ben
Schwendener, and of course George Russell himself have evidence of the way the
Lydian Chromatic Concept has served as a catalyst for great music destined to
stand the test of time.

I told you we’d have a lot of fun. Thanks for
listening. Check out Russell’s book, and remember that it is only the tip of
the Lydian Chromatic iceberg. Do your best to prove me wrong. I look forward to
the fruits of humanity’s continuing cultural, intellectual, and philosophical
evolution.

Bobby Spellman, November 2014

w

[1] That music
was bebop and other styles of jazz being played in New York in the 1940’s and
‘50’s. While the Lydian Chromatic Concept is a theory of all Western music and
not only American jazz, I suspect the fact that improvised music requires each
performer to be a spontaneous composer contributed largely to bringing these
anomalies in conventional theory to light. This is a story for another time.

[2]It is important to note that one can eat well
without studying nutrition, one can build a trebuchet without studying physics,
and one can write amazing music without any knowledge of music theory. Theories
are not always mandatory in practical matters, but they help by taking the
often time consuming guesswork out of the process.

[3] For this
reason I specify that it is a theory of Western music, though the fundamental implications could be applied to any
style of music the world over.

[4] I find
myself consistently aggravated by the term “avoid note,” and one thing I like
about the Lydian Chromatic Concept is that it eliminates the need for such a
ridiculous concept. I use it here for illustration, and I promise never to use
it again.

[5] This joke
will quickly become antiquated, and is likely to be excluded from future
editions.

[6] I lied about
never using the term again. Again, it’s only for clarity and explanation.

[7] I should add
that the sound of the blues has a rich and important tradition, and much could
be said about its West African origins, its cultural significance, and its
place at the root of American popular music. This is a story for another time, and
for now I’ll have to stick to a purely practical theoretical overview.

[8]Please note that as we get into more unusual
modes, I may fabricate some mode names based on what seems logical. I didn’t
know the number for the Bureau of Official Unconventional Mode Names, and I
figure a mode by any other name should sound as sweet.

4 comments:

It has been brought to my attention (thanks Remy and Kyle) that the music notation font that I was using to include sharp, flat, and natural signs was not registering on most computers and phones. As a result, accidentals were being very confusingly represented as J's and X's and G's and all kinds of terrible stuff. I've replaced the font so that best case scenario, it'll show up on your screen as music notation, and worse case, flats will be "b", sharps will be "#", and naturals will be "n". That should clear up any unnecessary confusion. Lord knows there's already enough necessary confusion.

Hi Bobby and greetings from Ireland,WOW, what a fantastic, well explained article.Just what I've been searching for: an understandable summary to help me decide if I should delve further in to this concept.You have me hooked now :)Thank you.

I have some questions (if you have the time) regarding your words quoted below:

Does the Lydian #1 note occur *anywhere* in the overtone series? (I assume it must?)If yes, do you know where in the tonal gravity order (I'm guessing last but I can't explain why) and where in the overtone series order?If no, then could we consider The Lydian Chromatic scale to only contain 11 notes?Also if no, do you know why not, or could you point to any further online reading on the subject?

..."you’ll notice that after B, we skip a fifth and end up on C#, the #5, rather than F#........This hiccup in the tonal spectrum would be impossible to explain within the reasonable confines of this still fairly innocuous article, but I’ll summarize the oddity by saying that it is a compromise that must be made for the twelve-tone equal temperament that serves as the foundation of our Western harmonic language. To further clarify, Western music as we know it depends on making adjustments to the natural overtone series and dividing the octave into 12 equal parts so we can do fancy stuff like play in tune over multiple octaves. This leap in the tonal order accounts for this, and makes sense sonically in the long run. For now you’ll just have to trust me."

Hi Bobby and greetings from Ireland,WOW, what a fantastic, well explained article.Just what I've been searching for: an understandable summary to help me decide if I should delve further in to this concept.You have me hooked now :)Thank you.

I have some questions (if you have the time) regarding your words quoted below:

Does the Lydian #1 note occur *anywhere* in the overtone series? (I assume it must?)If yes, do you know where in the tonal gravity order (I'm guessing last but I can't explain why) and where in the overtone series order?If no, then could we consider The Lydian Chromatic scale to only contain 11 notes?Also if no, do you know why not, or could you point to any further online reading on the subject?

..."you’ll notice that after B, we skip a fifth and end up on C#, the #5, rather than F#........This hiccup in the tonal spectrum would be impossible to explain within the reasonable confines of this still fairly innocuous article, but I’ll summarize the oddity by saying that it is a compromise that must be made for the twelve-tone equal temperament that serves as the foundation of our Western harmonic language. To further clarify, Western music as we know it depends on making adjustments to the natural overtone series and dividing the octave into 12 equal parts so we can do fancy stuff like play in tune over multiple octaves. This leap in the tonal order accounts for this, and makes sense sonically in the long run. For now you’ll just have to trust me."